Algorithmic Solution And Comparison Of Portfolio Related Models Under Utility Maximization

With the continuous development of the era,China's economic system has changed a lot.The original investment structure has changed a lot.The public's investment concept has more developed from the original physical investment to financial investment.Financial investment has become an essential skill for people.This also drives the continuous and healthy development of the current financial investment industry in China.Portfolio optimization is a major research direction of financial investment,means that investors allocate their own funds to several types of financial assets,so that the actual investment amount of various financial assets reach a certain percentage,so as to achieve the purpose of diversifying investment risks and ensuring expected return.Therefore,it is necessary to understand the investment market and theory,and learn some method of portfolio optimization.Portfolio research has a long history.There are two main analysis frameworks:the first is the expected utility maximization model;the other is the return-risk model.Different investment models have different application scenarios and optimization effects.This paper studies two different portfolio models,respectively named lottery dependent utility model and prospect theory utility model.They are combined with an improved particle swarm optimization algorithm under utility maximization to conduct empirical research and analysis results in multiple dimensions;and then add loss aversion in both models,to explore the utility function characteristics of two different models under the degree of monotone risk aversion.Through this research,I hope can help investors understanding of different investment portfolio models,provide some reference suggestions for the investors' investment behavior and play a positive role in China's financial investment market.